Evaluate Returns: Part 1
Kerry Back

Overview
- Suppose we’ve run a backtest and saved the portfolio returns.
- Evaluate raw returns: accumulation, drawdowns, mean, std dev, Sharpe ratio
- Evaluate relative to benchmarks
- Compare to the market on a beta-adjusted basis
- Compare to the market and other factors (attribution analysis)
Example returns
- Best 200 stocks each month, equally weighted
- Worst 200 stocks each month, equally weighted
- 150/50 portfolio = 1.5 \(\times\) best - 0.5 \(\times\) worst
- Market return from French’s data library
Accumulation plots
- (1+ret).cumprod()
- Also on log scale
Drawdowns
- A drawdown occurs whenever your portfolio value is not as high as it once was
- The percent drawdown is (current value - prior max) / prior max.
Statistics
- mean and std dev of monthly returns
- annualize mean by \(\times\) 12
- annualize std dev by \(\times\) sqrt(12)
- compute monthly excess returns (in excess of T-bill rate), mean and std dev and Sharpe ratio = mean / std dev
- annualize Sharpe ratio by \(\times\) sqrt(12)